arrow_backBack to Study Resources

Quiz Chapter 7: Measures of Dispersion for Grouped Data

10 questions · Form 5 Mathematics Bab 7: Measures of Dispersion for Grouped Data

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. If total frequency N = 80, at what cumulative frequency do you locate the third quartile (Q₃) on an ogive?

  1. C. 60
  2. A. 20
  3. B. 40
  4. D. 75
Show answer

Answer: C

Q₃ corresponds to (34) × N = (34) × 80 = 60.

2. Which graph MUST start at zero on the y-axis at the lower boundary of the first class interval?

  1. A. Ogive
  2. B. Histogram
  3. C. Scatter plot
  4. D. Bar chart
Show answer

Answer: A

An ogive begins at cumulative frequency 0 at the lower boundary of the first class interval.

3. What is the midpoint of the class interval 40 - 48?

  1. A. 44
  2. B. 44.5
  3. C. 40
  4. D. 48
Show answer

Answer: A

Midpoint x = Lower limit + Upper limit2 = 40 + 482 = 44.

4. In a grouped data table with class intervals 10-14, 15-19, 20-24, what is the lower boundary of the starting point on an ogive?

  1. B. 9.5
  2. A. 10
  3. C. 14.5
  4. D. 0
Show answer

Answer: B

An ogive starts at cumulative frequency 0 at the lower boundary of the first class interval (10 - 0.5 = 9.5).

5. Given ∑fx = 450 and ∑f = 30, calculate the mean x̄ of the grouped data.

  1. A. 15
  2. B. 12
  3. C. 18
  4. D. 20
Show answer

Answer: A

Mean x̄ = ∑fx / ∑f = 45030 = 15.

6. If all frequencies in a grouped dataset are multiplied by a constant factor of 2, what happens to the mean x̄?

  1. A. The mean remains unchanged
  2. B. The mean is multiplied by 2
  3. C. The mean is multiplied by 4
  4. D. The mean is halved
Show answer

Answer: A

Multiplying frequencies uniformly scales total frequency ∑f and ∑fx by 2, leaving mean x̄ = 2∑fx2∑f unchanged.

7. The interquartile range of a grouped dataset is defined as:

  1. A. Q₃ - Q₁
  2. B. Q₃ - Q₂
  3. C. Q₂ - Q₁
  4. D. Max value - Min value
Show answer

Answer: A

Interquartile range = Third Quartile (Q₃) - First Quartile (Q₁).

8. Which measure of dispersion is affected by every score in a grouped dataset and measured in squared units?

  1. B. Variance
  2. A. Interquartile range
  3. C. Standard deviation
  4. D. Range
Show answer

Answer: B

Variance measures the mean of squared deviations from the mean and is expressed in square units.

9. What is the standard deviation σ for a dataset with a variance of 16?

  1. A. 4
  2. B. 256
  3. C. 8
  4. D. 2
Show answer

Answer: A

Standard deviation σ = √Variance = √16 = 4.

10. When constructing a frequency polygon directly from a histogram, line segments connect:

  1. A. Midpoints of the top of adjacent bars
  2. B. Upper boundaries of adjacent bars
  3. C. Lower boundaries of adjacent bars
  4. D. Top-left corners of adjacent bars
Show answer

Answer: A

A frequency polygon connects the midpoints of the top edges of histogram bars.

Sponsored